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- /* specfunc/hyperg_0F1.c
- *
- * Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
- *
- * This program is free software; you can redistribute it and/or modify
- * it under the terms of the GNU General Public License as published by
- * the Free Software Foundation; either version 3 of the License, or (at
- * your option) any later version.
- *
- * This program is distributed in the hope that it will be useful, but
- * WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
- * General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with this program; if not, write to the Free Software
- * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
- */
- /* Author: G. Jungman */
- #include "gsl__config.h"
- #include "gsl_math.h"
- #include "gsl_errno.h"
- #include "gsl_sf_exp.h"
- #include "gsl_sf_gamma.h"
- #include "gsl_sf_bessel.h"
- #include "gsl_sf_hyperg.h"
- #include "gsl_specfunc__error.h"
- #define locEPS (1000.0*GSL_DBL_EPSILON)
- /* Evaluate bessel_I(nu, x), allowing nu < 0.
- * This is fine here because we do not not allow
- * nu to be a negative integer.
- * x > 0.
- */
- static
- int
- hyperg_0F1_bessel_I(const double nu, const double x, gsl_sf_result * result)
- {
- if(x > GSL_LOG_DBL_MAX) {
- OVERFLOW_ERROR(result);
- }
- if(nu < 0.0) {
- const double anu = -nu;
- const double s = 2.0/M_PI * sin(anu*M_PI);
- const double ex = exp(x);
- gsl_sf_result I;
- gsl_sf_result K;
- int stat_I = gsl_sf_bessel_Inu_scaled_e(anu, x, &I);
- int stat_K = gsl_sf_bessel_Knu_scaled_e(anu, x, &K);
- result->val = ex * I.val + s * (K.val / ex);
- result->err = ex * I.err + fabs(s * K.err/ex);
- result->err += fabs(s * (K.val/ex)) * GSL_DBL_EPSILON * anu * M_PI;
- return GSL_ERROR_SELECT_2(stat_K, stat_I);
- }
- else {
- const double ex = exp(x);
- gsl_sf_result I;
- int stat_I = gsl_sf_bessel_Inu_scaled_e(nu, x, &I);
- result->val = ex * I.val;
- result->err = ex * I.err + GSL_DBL_EPSILON * fabs(result->val);
- return stat_I;
- }
- }
- /* Evaluate bessel_J(nu, x), allowing nu < 0.
- * This is fine here because we do not not allow
- * nu to be a negative integer.
- * x > 0.
- */
- static
- int
- hyperg_0F1_bessel_J(const double nu, const double x, gsl_sf_result * result)
- {
- if(nu < 0.0) {
- const double anu = -nu;
- const double s = sin(anu*M_PI);
- const double c = cos(anu*M_PI);
- gsl_sf_result J;
- gsl_sf_result Y;
- int stat_J = gsl_sf_bessel_Jnu_e(anu, x, &J);
- int stat_Y = gsl_sf_bessel_Ynu_e(anu, x, &Y);
- result->val = c * J.val - s * Y.val;
- result->err = fabs(c * J.err) + fabs(s * Y.err);
- result->err += fabs(anu * M_PI) * GSL_DBL_EPSILON * fabs(J.val + Y.val);
- return GSL_ERROR_SELECT_2(stat_Y, stat_J);
- }
- else {
- return gsl_sf_bessel_Jnu_e(nu, x, result);
- }
- }
- /*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/
- int
- gsl_sf_hyperg_0F1_e(double c, double x, gsl_sf_result * result)
- {
- const double rintc = floor(c + 0.5);
- const int c_neg_integer = (c < 0.0 && fabs(c - rintc) < locEPS);
- /* CHECK_POINTER(result) */
- if(c == 0.0 || c_neg_integer) {
- DOMAIN_ERROR(result);
- }
- else if(x < 0.0) {
- gsl_sf_result Jcm1;
- gsl_sf_result lg_c;
- double sgn;
- int stat_g = gsl_sf_lngamma_sgn_e(c, &lg_c, &sgn);
- int stat_J = hyperg_0F1_bessel_J(c-1.0, 2.0*sqrt(-x), &Jcm1);
- if(stat_g != GSL_SUCCESS) {
- result->val = 0.0;
- result->err = 0.0;
- return stat_g;
- }
- else if(Jcm1.val == 0.0) {
- result->val = 0.0;
- result->err = 0.0;
- return stat_J;
- }
- else {
- const double tl = log(-x)*0.5*(1.0-c);
- double ln_pre_val = lg_c.val + tl;
- double ln_pre_err = lg_c.err + 2.0 * GSL_DBL_EPSILON * fabs(tl);
- return gsl_sf_exp_mult_err_e(ln_pre_val, ln_pre_err,
- sgn*Jcm1.val, Jcm1.err,
- result);
- }
- }
- else if(x == 0.0) {
- result->val = 1.0;
- result->err = 1.0;
- return GSL_SUCCESS;
- }
- else {
- gsl_sf_result Icm1;
- gsl_sf_result lg_c;
- double sgn;
- int stat_g = gsl_sf_lngamma_sgn_e(c, &lg_c, &sgn);
- int stat_I = hyperg_0F1_bessel_I(c-1.0, 2.0*sqrt(x), &Icm1);
- if(stat_g != GSL_SUCCESS) {
- result->val = 0.0;
- result->err = 0.0;
- return stat_g;
- }
- else if(Icm1.val == 0.0) {
- result->val = 0.0;
- result->err = 0.0;
- return stat_I;
- }
- else {
- const double tl = log(x)*0.5*(1.0-c);
- const double ln_pre_val = lg_c.val + tl;
- const double ln_pre_err = lg_c.err + 2.0 * GSL_DBL_EPSILON * fabs(tl);
- return gsl_sf_exp_mult_err_e(ln_pre_val, ln_pre_err,
- sgn*Icm1.val, Icm1.err,
- result);
- }
- }
- }
- /*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/
- #include "gsl_specfunc__eval.h"
- double gsl_sf_hyperg_0F1(const double c, const double x)
- {
- EVAL_RESULT(gsl_sf_hyperg_0F1_e(c, x, &result));
- }
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